Purchases I made on iOS are not showing up as downloadable on my computers

Music purchases I made on iOS are not showing up as downloadable on either of my computers (OS X and Win 7), even though they are both set to show cloud content. When I go into the store on the desktop iTunes, the items show as "purchased" but do not say "play" and do not give me the option of downloading. I've tried closing and restarting iTunes already, and it doesn't help.